Best Known (152−41, 152, s)-Nets in Base 4
(152−41, 152, 531)-Net over F4 — Constructive and digital
Digital (111, 152, 531)-net over F4, using
- 4 times m-reduction [i] based on digital (111, 156, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 52, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 52, 177)-net over F64, using
(152−41, 152, 1047)-Net over F4 — Digital
Digital (111, 152, 1047)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4152, 1047, F4, 41) (dual of [1047, 895, 42]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0) [i] based on linear OA(4151, 1025, F4, 41) (dual of [1025, 874, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1025 | 410−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 21 step Varšamov–Edel lengthening with (ri) = (1, 20 times 0) [i] based on linear OA(4151, 1025, F4, 41) (dual of [1025, 874, 42]-code), using
(152−41, 152, 97199)-Net in Base 4 — Upper bound on s
There is no (111, 152, 97200)-net in base 4, because
- 1 times m-reduction [i] would yield (111, 151, 97200)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 8 148360 458425 218598 060128 839829 723014 682615 385376 754308 952654 155384 594485 300369 415204 221786 > 4151 [i]